Basis of Fuzzy Generalized Topological Space

This paper studies the concept of fuzzy generalized topologies, which are generalizations of smooth topologies and Chang’s fuzzy topologies. A basis of fuzzy generalized topological space will be defined as functions from the family of all fuzzy subsets of a non-empty set X to [0, 1] and some basic properties of their struc-ture will be obtained. Some characterizations of the basis of fuzzy generalized topology, fuzzy generalized cotopology and the product of fuzzy generalized topological spaces will also be shown.